File under Gq, Glr, and Gr as per CHC model
Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval? ☆
Highlights
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- It is universally assumed that the answer of small additions is retrieved from memory.
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- Contrariwise, we replicate that they are solved by automated compacted procedures.
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- Moreover, we show here that these procedures are limited to operands up to 4.
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- Counterintuitively, RTs suggest that retrieval could be used for larger additions.
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- Compacted procedures are faster than retrieval and consequently mistaken for it.
Abstract
Contrary
to a widespread assumption, a recent study suggested that adults do not
solve very small additions by directly retrieving their answer from
memory, but rely instead on highly automated and fast counting
procedures (Barrouillet & Thevenot, 2013).
The aim of the present study was to test the hypothesis that these
automated compiled procedures are restricted to small quantities that do
not exceed the size of the focus of attention (i.e., 4 elements). For
this purpose, we analyzed the response times of ninety adult
participants when solving the 81 additions with operands from 1 to 9.
Even when focusing on small problems (i.e. with sums ⩽10) reported by
participants as being solved by direct retrieval, chronometric analyses
revealed a strong size effect. Response times increased linearly with
the magnitude of the operands testifying for the involvement of a
sequential multistep procedure. However, this size effect was restricted
to the problems involving operands from 1 to 4, whereas the pattern of
response times for other small problems was compatible with a retrieval
hypothesis. These findings suggest that very fast responses routinely
interpreted as reflecting direct retrieval of the answer from memory
actually subsume compiled automated procedures that are faster than
retrieval and deliver their answer while the subject remains unaware of
their process, mistaking them for direct retrieval from long-term memory.
